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Sylvester

Syntax

Sylvester(F:POLY,G:POLY,X:INDET)
    

Summary

the Sylvester matrix of two polynomials

Description

This function returns the Sylvester matrix of the polynomials F and G with respect to the indeterminate X. This is the matrix used to calculate the resultant.

example

    
Use R ::= Q[p,q,x];
F := x^3+px-q; G := Der(F,x);
Sylvester(F,G,x);
Mat[
  [1, 0, p, -q, 0],
  [0, 1, 0, p, -q],
  [3, 0, p, 0, 0],
  [0, 3, 0, p, 0],
  [0, 0, 3, 0, p]
]
-------------------------------
Det(Sylvester(F,G,x)) = Resultant(F,G,x);
TRUE
-------------------------------
        
    

See Also